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Abstract
Based on non-collinear phase-matching (PM), a new method for widely tunable wavelength was proposed and demonstrated in a four-mirror ring cavity of non-critical phase-matching (NCPM) KTiOAsO4 (KTA) optical parametric oscillator (OPO). Wavelength tuning range of 141 nm from 1535.56 nm to 1676.73 nm was achieved by moving one mirror of ring cavity back and forth. The tuning theory and tuning method of non-collinear PM were analyzed in detail. The output energy and pulse width of signal were measured and compared in collinear and non-collinear PM condition. This method is also applicable to OPOs of other nonlinear crystals based on four-mirror ring cavity.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Eye-safe wavelengths refer to the operating wavelengths of the laser exceeding 1400 nm (mid infrared to far infrared), which are widely applied in remote monitoring of atmospheric gases, laser lidar and optical communication, etc [1–3]. Commonly methods used to generate eye-safe wavelength include rare-earth ions doped crystal, Raman laser and optical parametric oscillator (OPO) [4–7].
For all-solid-state laser, OPO is widely used in the generation of high energy eye-safe wavelength and wavelength tuning technology is usually applied to achieve large-range wavelength output. Temperature tuning [8,9] and angle tuning methods [10] are usually employed in realizing wavelength tunable for OPO, such as periodically poled crystal (MgO:PPLN, PPKTA, PPKTP, etc) [11–15], birefringence phase-matching crystal with critical phase-matching (KTP, KTA, ZGP, etc) [16–20]. However, for high energy OPO laser, non-critical phaser-matching (NCPM) is preferred. Because NCPM has large effective nonlinear coefficient, large acceptable angle of incidence and no walk-off effect, thus NCPM nonlinear crystal is more suitable for generating high-energy parametric light. Based on NCPM-KTA crystal, our team has achieved a parametric light output energy with 242 mJ and 43.6% conversion efficiency in a plane-parallel cavity [21]. However, the wavelength tuning range is very small under collinear phase-matching (PM) condition. To realize large-range wavelength tuning for NCPM, Zhong kai et al. reported a method of non-collinear PM, which can be realized by changing the signal oscillation path [22] or the pump transmission path [23]. Changing the pump transmission path is not suitable for high energy pumping system, which will cause air ionization due to the focusing effect of 4f imaging system. As reported, by changing the signal oscillation direction, a wavelength tuning range about 110 nm was realized by rotating a cavity mirror under an isosceles-right-triangle three-mirror ring cavity [22]. Since the rotating angle of mirror is very small, collinear parametric oscillation can still be generated. Moreover, the angle and position of the mirror need to be slightly tuned, which increases the complexity of experimental operation and the instability of resonator.
In this paper, a new method in a four-mirror ring cavity for realizing wide tuning range of NCPM-KTA OPO is proposed and achieved based on non-collinear PM. Through the analysis of the cavity structure, signal singly resonant OPO under non-collinear state is realized by adjusting a cavity mirror. The theoretical tuning curve is calculated by analyzing corresponding equations in non-collinear PM condition. Compared with angle-tuning method by rotating crystal, the wavelength tuning range of non-collinear PM is much wider. In addition, the output energies and pulse widths are measured and analyzed in collinear and non-collinear condition.
2. Experimental setup
Based on NCPM-KTA crystal, the experimental setup of non-collinear PM in a four-mirror ring cavity is shown in Fig. 1. A homemade high-energy 1064 nm laser with pulse repetition rate of 100 Hz and pulse width of 20 ns was used as the pump source of NCPM-KTA OPO. A plano-convex lens (L1) and a plano-concave lens (L2) were composed to collimate the pump beam. The focal lengths of L1 and L2 were 400 mm and −300 mm respectively. The beam diameter of 1064 nm pump light was set to 5 mm by adjusting the distance between L1 and L2. As 45° OPO input mirror, M1 was coated with 1064 nm high transmittance (HT) and 1.5 µm high reflectivity (HR). The coating parameters of M2 and M3 were identical with M1. The 45° OPO output mirror (OC) M4 was coated with 1064 nm HT and 1.5 µm partial transmittance (T = 50%). In order to improve the OPO conversion efficiency and reduce the oscillation threshold, a double-pass pumping configuration of four-mirror ring cavity was designed by using a 0° 1064 nm HR mirror (M5). Limited by the output mirror in hand, the output parameters of OPO under different transmittances had not been measured. An X-cut NCPM-KTA crystal (θ = 90°, φ = 0°) was used as nonlinear crystal with a size of 9.5 × 9.5 × 30 mm3. M3 was mounted on a one-dimension displacement platform to move its position for realizing wavelength tunable. The KTA crystal was not coated with film, which would cause partially loss of pump energy. Based on the measured values of transmittance, the corresponding calculated [24] absorption coefficients were 0.004 cm−1 at 1064 nm and 0.011 cm−1 at 1535 nm, respectively. The distance between M1 and M2 was 55 mm and the distance between M2 and M3 was 40 mm, so the physical cavity length of four-mirror ring cavity was 190 mm.
Fig. 1. The experimental setup diagram of noncollinear phase matching of NCPM-KTA crystal four-mirror ring cavity. L1: convex lens; L2: concave lens; M1, M2 and M3: 45° OPO input mirror; M4: 45° output mirror; M5:0° 1064 nm HR mirror.
3. Theoretical and tuning method analysis
According to the condition of energy conservation and momentum conservation, the PM of three-wave interaction is expressed as:
The schematic diagram of non-collinear PM in X-Z principal plane is depicted in Fig. 2. For non-collinear PM condition, the relationship between wavelength and refractive index is:
Fig. 2. The schematic diagram of the geometry of non-collinear phase-matching. α: the angle between pump and signal; β: the angle between pump and idler.
For type-ΙΙ PM (o$\to $o + e) condition, the three-wave interactions of biaxial KTA crystal occur in X-Z plane (φ = 0°), so the equation of refractive index curve is:
According to Eq. (3), Eq. (5) and the Sellmeier equations of KTA crystal referred to Ref. [25], the sine value of the phase-matching angle is expressed as [26]:
Based on Eq. (1) to Eq. (6), the signal wavelength tuning curves under collinear and non-collinear PM conditions are calculated and described in Fig. 3. When the non-collinear angle is 5°, the signal wavelength changes from 1534 nm to 1792nm, achieving 258 nm tuning range. However, under the same variation of angle, angle tuning only achieves a tuning range less than 4 nm [25].
Fig. 3. The tuning curves of signal wavelength at collinear phase-matching and noncollinear phase-matching. (a) angle tuning; (b) noncollinear tuning.
To better understand the tuning method, the schematic diagram of non-collinear PM wavelength tuning in a four-mirror ring cavity is depicted in Fig. 4. The oscillation path of signal is a rectangular in collinear PM condition, while it is a parallelogram in non-collinear PM condition. When the propagation direction of signal deviates from pump by ψ degrees in crystal, the propagation path of signal does not intersect on M3, resulting in no oscillation for signal. However, the propagation path of signal will form an intersection point near M3, so if M3 is moved to the intersection point, the signal light can oscillate in the cavity. According to the description of Fig. 4, the signal wavelength tuning can be realized by moving M3 without changing the angle of M3. In order to reduce the oscillation threshold, M3 is moved forward in this experiment, choosing a shorter oscillation path.
Fig. 4. The schematic diagram of four-mirror ring cavity for non-collinear phase-matching wavelength tuning by moving M3. The inset shows the variation of propagation path of signal inside and outside the crystal.
4. Experimental results and discussion
As shown in Fig. 5, the signal wavelengths at different displacement distances were measured by an Optical Spectrum Analyzer (YOKOGAWA, AQ6370D). Since the angle between pump and signal outside the crystal $\psi ^{\prime}$ was same as the deviated angle of output signal light, the angle of $\psi ^{\prime}$ at different displacement distances were measured by measuring the displacement distance of signal beam when the distance between measuring point and M4 was far enough. The noncollinear angle inside the crystal $\psi$ needed to be calculated by considering the refractive index parameters of crystal for signal based on the refractive index formula. According to the measured values of noncollinear angle, the corresponding theoretical curve of signal wavelength was calculated through the equations in section 3. By linear fitting method, the relationship between displacement distance and noncollinear angle was denoted by the equation inserted in Fig. 5. When the displacement distance was increased from 0 to 10 mm, the output wavelength of signal varied from 1535.6 nm to 1627.3 nm, corresponding to the noncollinear angle range of 0° to 2.85°.
Fig. 5. The signal wavelength and noncollinear angle vs. displacement distance. The black line is the theoretical signal wavelength at different distances; the blue point is the measured signal wavelength at different distances.
The output energies of signal are depicted in Fig. 6 at different signal wavelengths. The maximum output energy was 23.5 mJ at 1535.6 nm with 236 mJ pump energy, corresponding to a conversion efficiency (pump to signal) of 9.96%. Due to the growth quality of crystal, long cavity length and beam profile of pump light, the conversion efficiency was lower than our previous result [21], which could be improved by optimizing the beam profile of pump light and using high quality crystal. Because the mirror of cavity was not coated with film at 3.5 µm, in theory, the generated idler light transmitted through M2 and M5. To make the experimental measurement results more accurate, a 1.5 µm and 3.5 µm dichroic mirror was placed after the output parametric light. The results indicate that the output energy of signal gradually decreased as the signal wavelength increased (corresponding to the increased noncollinear angle). The output energy decreased to 1.2 mJ at 1586.5 nm. Since the output energy of the longer signal wavelength was small, its data was not measured.
As shown in Fig. 7, the output pulse-shape was measured by an InGaAs photodetector and an oscilloscope (MSO64B, Tektronix). The pulse width (full width at half maximum, FWHM) of pulse shape of signal at 1540.5 nm was 18.37 ns under collinear PM condition with 236 mJ pump, as shown in Fig. 7(a). With the same pump energy and wavelength, the pulse width (FWHM) under non-collinear PM condition is 13.81 ns shown in Fig. 7(b). Compared with collinear PM, non-collinear PM cannot coincide well with the pump beam and signal beam in space, resulting in incomplete mode matching. Similar to the walk-off effect, the parametric light conversion effect will be affected, which become more serious with the increase of non-collinear angle [27]. Therefore, the threshold of non-collinear PM is higher than collinear PM and higher intensity pump is required to generate signal pulse, resulting in narrower pulse width of signal.
Fig. 7. The output pulse shape of signal. (a) collinear phase-matching oscillation for output signal wavelength 1535.6 nm; (b) non-collinear phase-matching oscillation for output signal wavelength 1540.5 nm.
In experiment, a near-infrared CCD (SP620U-MIR, Ophir) was used to observe the beam profile of signal and measure the beam spot size. As shown in Fig. 8, the M 2 factors were Mx2 = 8.83, My2 = 9.33 in collinear PM (1535.6 nm, 23.5 mJ) and Mx2 = 4.37, My2 = 3.79 (1540.5 nm, 15.8 mJ), Mx2 = 8.66, My2 = 4.27 (1545.5 nm, 9.4 mJ), Mx2 = 5.68, My2 = 2.38 (1553.5 nm, 4.5 mJ) in non-collinear PM. The insets show the beam profile of signal at focus position. The value of beam quality M2 of signal decreased from collinear (1535.6 nm) to non-collinear (1540.5 nm), however, there was an unexpected increase at 1545.5 nm and then continued to decrease.
Fig. 8. The beam quality of signal under different PM condition. (a) collinear PM at 1535.6 nm; (b) non-collinear PM at 1540.5 nm; (c) non-collinear PM at 1545.5 nm; (d) non-collinear PM at 1553.5 nm; (e) the directions of pump and signal inside the crystal under ideal and real conditions. The insets show the beam profile of signal at focus position.
Normally, as the non-collinear angle between signal light and pump light increased, the effective length of nonlinear crystal would decrease, resulting in increased intra-cavity loss and better beam quality of signal. However, the oscillation path of signal may not be identical with the theoretical description, which was caused by the deviation in the construction of four-mirror cavity, as shown in Fig. 8(e). The plane formed by signal and pump propagation path was not parallel to the x-axis of crystal, but had an angle, so the beam profile of signal was an oblique ellipse and the beam quality of signal abruptly changed during our experiment. In experiment, when M3 was moved back and forth in experiment, we found that the output energy of signal could be enhanced by slightly adjusting M2, which also affected the oscillation direction of signal in the cavity.
In order to clearly distinguish the spectrum distribution, the measured data were processed by normalizing the intensity and nulling noise. The measured signal wavelength tuning range is described in Fig. 9. The maximum tuning range was about 141.1 nm (from 1535.56 nm to 1676.73 nm). Since the measurement range of the Optical Spectrum Analyzer was 600 nm−1700nm, the noise was so large around 1700nm that the signal was not displayed. For noncollinear phase matching, as the non-collinear angle increases, the phase mismatch Δk increases, resulting in an increase of the linewidth of signal. As the non-collinear angle increased, the signal wavelength was moved toward the long wave band, and the linewidth of signal was broadened [23,28]. Limited by the output energy, the spectral linewidths were measured at several wavelengths. The corresponding spectrum linewidths of signal are 0.27 nm at 1535.8 nm, 0.40 nm at 1539.6 nm, 0.50 nm at 1544.3 nm, 0.63 nm at 1550.2 nm and 0.73 nm at 1557.3 nm respectively, and the trend is consistent with previous theoretical and experimental results [23,28].
5. Conclusion
In summary, a widely tunable NCPM-KTA OPO for eye-safe wavelength was demonstrated in a four-mirror ring cavity. Based on the configuration of cavity, a novel method for non-collinear PM wavelength tuning was firstly proposed and realized by moving only one mirror. According to the theoretical equations, the relationship between displacement distance and non-collinear angle was obtained. The signal wavelength tuning range of 141 nm was achieved from 1535.56 nm to 1676.73 nm. The output energy of signal in collinear PM was 23.5 mJ, and the corresponding optical-optical conversion efficiency from pump to signal was 9.96%. The beam qualities of signal at different PM conditions were measured and analyzed, and the beam profile of signal was observed and compared. The pulse widths of collinear PM and non-collinear PM were measured, which indicated that the pulse width of non-collinear PM was narrower than collinear PM. We believe that the output characteristics will be improved after promoting the quality of crystal and parameters of cavity.
Funding
Key research program of Shandong Province (2020JMRH0302); National Natural Science Foundation of China (62075116, 62075117); Natural Science Foundation of Shandong Province (ZR2019MF039, ZR2020MF114, ZR2022QF087); China Postdoctoral Science Foundation (2021TQ0190); Postdoctoral Innovation Foundation of Shandong Province (SDCX-ZG-202202014); Founding for Qilu Young Scholars from Shandong University.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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